{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<h1 align=\"center\"> Explaining Box Plots </h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I was always curious about where the -2.698σ,  -.6745σ, 6745σ, and 2.698σ numbers came from. Consequently I would look it up and find they are from Z Score Tables which are basically tables showing the percentages of numbers coming up in a normal. This post will derive a Z Score table and explain the different parts of a box plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook explains how those numbers were derived in the hope that they can be more interpretable for your future endeavors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import all libraries for the rest of the blog post\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "from matplotlib.patches import ConnectionPatch\n",
    "from scipy.integrate import quad\n",
    "import pandas as pd\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B1m9MkPUQR5CJiIiqNo4g6zfeFT3EBJmIiKhq4wiyfmOCrIeYIBMREVVt8hFk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\nDAAAAAQIyAAAAEDg/wGl4nvOoIwWqAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150c38ecd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize=(10, 5))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes.boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes.set_xlim(-4, 4)\n",
    "plt.xticks(fontsize = 14)\n",
    "\n",
    "axes.set_yticks([])\n",
    "axes.annotate(r'',\n",
    "            xy=(-.73, .205), xycoords='data',\n",
    "            xytext=(.66, .205), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes.text(0, .25, \"Interquartile Range \\n(IQR)\",  horizontalalignment='center', fontsize=18)\n",
    "axes.text(0, -.21, r\"Median\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(2.65, -.15, \"\\\"Maximum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.15, \"\\\"Minimum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-.68, -.24, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.21, r\"(Q1 - 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(.6745, -.24, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(.6745, -.30, r\"(75th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(-.68, -.30, r\"(25th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(2.65, -.21, r\"(Q3 + 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes.annotate('Outliers', xy=(2.93,0.015), xytext=(2.52,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "axes.annotate('Outliers', xy=(-3.01,0.015), xytext=(-3.41,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/simple_boxplot.png', dpi = 2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.698"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((2 * .6745) * 1.5) + .6745"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6622499999999998"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stuff = (2.65 - .6745) / 2\n",
    ".6745 + stuff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Whiskers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The part in blue are the whiskers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ERK82jiDrNybIeogJMhER0auNI8j6jY+KHuIcZCIiolcbR5D1GxNkPcQRZCIi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\nDAAAAHgQkAEAAAAPAjIAAADg8X8YCdejjwWRPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c2c9b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize=(10, 5))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes.boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes.set_xlim(-4, 4)\n",
    "plt.xticks(fontsize = 14)\n",
    "\n",
    "axes.set_yticks([])\n",
    "axes.annotate(r'',\n",
    "            xy=(-.73, .205), xycoords='data',\n",
    "            xytext=(.66, .205), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes.text(0, .25, \"Interquartile Range \\n(IQR)\",  horizontalalignment='center', fontsize=18)\n",
    "axes.text(0, -.21, r\"Median\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(2.65, -.15, \"\\\"Maximum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "#axes.text(-1.66, .03, \"Whisker\", horizontalalignment='center', fontsize=18);\n",
    "\n",
    "axes.text(1.66, .06, r'Whisker', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white',\n",
    "                  'edgecolor':'blue',\n",
    "                  'linewidth': 4,\n",
    "                  'alpha': .4,\n",
    "                  'pad':10.0});\n",
    "\n",
    "axes.text(-1.66, .06, r'Whisker', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white',\n",
    "                  'edgecolor':'blue',\n",
    "                  'linewidth': 4,\n",
    "                  'alpha': .4,\n",
    "                  'pad':10.0});\n",
    "\n",
    "axes.text(-2.65, -.15, \"\\\"Minimum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-.68, -.24, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.21, r\"(Q1 - 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(.6745, -.24, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(.6745, -.30, r\"(75th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(-.68, -.30, r\"(25th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(2.65, -.21, r\"(Q3 + 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes.annotate('Outliers', xy=(2.93,0.015), xytext=(2.52,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "axes.annotate('Outliers', xy=(-3.01,0.015), xytext=(-3.41,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/simple_whisker.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting it All Together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "#Integrate PDF from -.6745 to .6745\n",
    "result_n67_67, _ = quad(normalProbabilityDensity, -.6745, .6745, limit = 1000)\n",
    "\n",
    "# Integrate PDF from -2.698 to -.6745\n",
    "result_n2698_67, _ = quad(normalProbabilityDensity, -2.698, -.6745, limit = 1000)\n",
    "\n",
    "# Integrate PDF from .6745 to 2.698\n",
    "result_67_2698, _ = quad(normalProbabilityDensity, .6745, 2.698, limit = 1000)\n",
    "\n",
    "# Integrate PDF from 2.698 to positive infinity\n",
    "result_2698_inf, _ = quad(normalProbabilityDensity, 2.698, np.inf, limit = 1000)\n",
    "\n",
    "# Integrate PDF from negative infinity to -2.698\n",
    "result_ninf_n2698, _ = quad(normalProbabilityDensity, np.NINF, -2.698, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ltCYAgLIgv8eVohx7UDAEQLhVpUoVde7UudCP2xd1fgBA+ZKf4wLHjtLDJWAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cc4e790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "\n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "# lower box\n",
    "con = ConnectionPatch(xyA=(-.6745, 0), xyB=(-.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper box\n",
    "con = ConnectionPatch(xyA=(.6745, 0), xyB=(.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# lower whisker\n",
    "con = ConnectionPatch(xyA=(-2.698, 0), xyB=(-2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper whisker\n",
    "con = ConnectionPatch(xyA=(2.698, 0), xyB=(2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -.6745, .6745\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-.6745, 0)] + list(zip(ix, iy)) + [(.6745, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "axes[1].text(0, .04, r'{0:.0f}%'.format(result_n67_67*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "##############################\n",
    "a, b = -2.698, -.6745# integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(-1.40, .04, r'{0:.2f}%'.format(result_n2698_67*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = .6745, 2.698 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(1.40, .04, r'{0:.2f}%'.format(result_67_2698*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = 2.698, 4 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(3.3, .04, r'{0:.2f}%'.format(result_2698_inf*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = -4, -2.698 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(-3.3, .04, r'{0:.2f}%'.format(result_ninf_n2698*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/boxplotNormalDistributionOverlay.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability Density Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be able to understand where the percentages come from in the 68-95-99.7 rule, it is important to know about the probability density function (PDF). A PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable’s PDF over that range — that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. This definition might not make much sense so let’s clear it up by graphing the probability density function for a normal distribution. The equation below is the probability density function for a normal distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the function is simpler, let’s graph this function with a range from -4 to 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RePLk7FyaJSdxUUafqhtLnbt8QhpFJaU8O29N1Y1FpMGJpaA7Eng+GGRQXs+c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\njBngrKAzxhhjjBng/gEf0xSI7vH/LwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10baea190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import all libraries for the rest of the blog post\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "fig, ax = plt.subplots(figsize=(10, 5));\n",
    "ax.plot(x, pdf_normal_distribution);\n",
    "ax.set_ylim(0);\n",
    "ax.set_title('Normal Distribution', size = 20);\n",
    "ax.set_ylabel('Probability Density', size = 20);\n",
    "fig.savefig('images/normalDistributionPDF.png', dpi = 900);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph above does not show you the probability of events but their probability density. To get the probability of an event within a given range we will need to integrate. Suppose we are interested in finding the probability of a random data point landing within 1 standard deviation of the mean, we need to integrate from -1 to 1. This can be done with SciPy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\Huge \\int_{-.6745}^{.6745}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.500006514273\n"
     ]
    }
   ],
   "source": [
    "# Make a PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -.6745 to .6745\n",
    "result_50p, _ = quad(normalProbabilityDensity,\n",
    "                     -.6745,\n",
    "                     .6745,\n",
    "                     limit = 1000)\n",
    "print(result_50p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JSI1VVFTEuAcfZN3cuQzt1SvucLLy20MO4fO33+bF//wn7lBEpIpTMiciNdaH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\nSRbMaIkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e219350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -.6745, .6745 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-.6745}^{.6745}f(x)\\mathrm{d}x=$\" + \"{0:.0f}%\".format(result_50p*100),\n",
    "         horizontalalignment='center', fontsize=11.5);\n",
    "\n",
    "ax.set_title(r'50% of Values are within .6745 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/interquartileRange.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "50% of the data is within .6745 standard deviation (σ) of the mean (μ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Showing IQR with Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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leXoZsh2kqq2zeBWug5KE3SbeV9Bfa5CCQdYHhYtnhWkWmVl8P8B9FbR4uqqn/1+d4+4F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\nF1sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b596090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "\n",
    "# 916170 is new seed\n",
    "# 39 was the seed\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=False, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'Red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='White', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='White'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes[0].set_title('50% of Values are within .6745$\\sigma$', fontdict = {'fontsize': 26, 'fontweight': 'medium'});\n",
    "\n",
    "\n",
    "\n",
    "#axes.set_title('Stuff', fontdict = {'fontsize': 29, \n",
    "#                                    'fontweight': 'bold'} )\n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "#axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "#axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "# lower box\n",
    "con = ConnectionPatch(xyA=(-.6745, 0), xyB=(-.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper box\n",
    "con = ConnectionPatch(xyA=(.6745, 0), xyB=(.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -.6745, .6745\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-.6745, 0)] + list(zip(ix, iy)) + [(.6745, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "\n",
    "axes[1].text(0, .04, r'{0:.0f}%'.format(result_50p*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/IQRboxplotDistribution.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\Huge \\int_{-2.698}^{2.698}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.993024255934\n"
     ]
    }
   ],
   "source": [
    "# Make a PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -2.698 to 2.698\n",
    "result_99_3p, _ = quad(normalProbabilityDensity,\n",
    "                     -2.698,\n",
    "                     2.698,\n",
    "                     limit = 1000)\n",
    "print(result_99_3p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UZu3atbzw6KPcN2YMO3btynEjR+Yl8SotK+OGF17go6VLOfKPf2TkHntQVBRn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\nKaVUFabFnFJKKaVUFfb/AXjM8zZ0cje5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b70f610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -2.698, 2.698 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-2.698}^{2.698}f(x)\\mathrm{d}x=$\" + \"{0:.1f}%\".format(result_99_3p*100),\n",
    "         horizontalalignment='center', fontsize=11.5);\n",
    "\n",
    "ax.set_title(r'99.3% of Values are within 2.698 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/99_3.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "99.3% of the data is within 2.698 standard deviations (σ) of the mean (μ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Showing Whiskers with Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+EREREY9RACgiIiLiMQoARURERDxGAaCIiIiIxygAFBEREfEYBYAiIiIiHqMA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37Ig6s+J1U7eL9fMTPincGulhBCtItNwZN9alicXEJxpZN/WfQxT7+3X1oDxTlJAijCgtaa17cf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\nhBBCCBFmJAEUQgghhAgz/w9z7C1Xnf/n4wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b5330d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# 8, 11, 20\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=False, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='red', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='red'),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes[0].set_title('99.3% of Values are within 2.698$\\sigma$', fontdict = {'fontsize': 26, 'fontweight': 'medium'});\n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "# lower whisker\n",
    "con = ConnectionPatch(xyA=(-2.698, 0), xyB=(-2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper whisker\n",
    "con = ConnectionPatch(xyA=(2.698, 0), xyB=(2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -2.698, 2.6988\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-2.698, 0)] + list(zip(ix, iy)) + [(2.698, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "axes[1].text(0, .04, r'{0:.1f}%'.format(result_99_3p*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/99_3_Distribution.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\Huge\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "# Make PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate from -inf to +inf\n",
    "result, _ = quad(normalProbabilityDensity,\n",
    "                     -np.inf,\n",
    "                     np.inf,\n",
    "                     limit = 1000)\n",
    "\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bb72lgQMHpoxv06aNOnXqpBYtWmjQoEGaNm1aqvmqVKmSUkuLFi0UGBioXr166ZtvvlHP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\nY4wpGBsAGmOMMcYUjA0AjTHGGGMK5v9gm6TxaVXy9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e5552d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='red', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='red'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='red', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -4, 4\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-.6745, 0)] + list(zip(ix, iy)) + [(.6745, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "axes[1].text(0, .04, r'{0:.0f}%'.format(result*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/combined100.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## New Stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VJSbiJCcm4qTXmIgTEVFVYiJOcmIiTnpLCMFEnIiIqhQTcZITE3HSW7dv30Z2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b91c5d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize=(10, 5))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes.boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "plt.xticks(fontsize = 14)\n",
    "\n",
    "axes.set_yticks([])\n",
    "axes.annotate(r'',\n",
    "            xy=(-.73, .205), xycoords='data',\n",
    "            xytext=(.66, .205), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes.text(0, .25, \"Interquartile Range \\n(IQR)\",  horizontalalignment='center', fontsize=18)\n",
    "axes.text(0, -.21, r\"Median\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(2.65, -.15, \"\\\"Maximum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.15, \"\\\"Minimum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-.68, -.24, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.21, r\"(Q1 - 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(.6745, -.24, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(.6745, -.30, r\"(75th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(-.68, -.30, r\"(25th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(2.65, -.21, r\"(Q3 + 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes.annotate('Outliers', xy=(2.93,0.015), xytext=(2.52,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "axes.annotate('Outliers', xy=(-3.01,0.015), xytext=(-3.41,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "fig.tight_layout()\n",
    "axes.set_xticks([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]);\n",
    "\n",
    "stuff = axes.get_xticklabels()\n",
    "\n",
    "xTickLabels = [r'$-5\\sigma$',\n",
    "               r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$',\n",
    "               r'$5\\sigma$'];\n",
    "\n",
    "axes.set_xticklabels(xTickLabels, fontsize = 18);\n",
    "\n",
    "\n",
    "\n",
    "#fig.savefig('images/simple_boxplot.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\Huge\\int_{-\\infty}^{\\infty}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "# Make PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate from -inf to +inf\n",
    "result, _ = quad(normalProbabilityDensity,\n",
    "                     -np.inf,\n",
    "                     np.inf,\n",
    "                     limit = 1000)\n",
    "\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ltCYAgLIgv8eVohx7UDAEQLhVpUoVde7UudCP2xd1fgBA+ZKf4wLHjtLDJWAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150eadfad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(916170)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "# lower box\n",
    "con = ConnectionPatch(xyA=(-.6745, 0), xyB=(-.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper box\n",
    "con = ConnectionPatch(xyA=(.6745, 0), xyB=(.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# lower whisker\n",
    "con = ConnectionPatch(xyA=(-2.698, 0), xyB=(-2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper whisker\n",
    "con = ConnectionPatch(xyA=(2.698, 0), xyB=(2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"black\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -.6745, .6745\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-.6745, 0)] + list(zip(ix, iy)) + [(.6745, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "axes[1].text(0, .04, r'{0:.0f}%'.format(result_n67_67*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "##############################\n",
    "a, b = -2.698, -.6745# integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(-1.40, .04, r'{0:.2f}%'.format(result_n2698_67*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = .6745, 2.698 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(1.40, .04, r'{0:.2f}%'.format(result_67_2698*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = 2.698, 4 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(3.3, .04, r'{0:.2f}%'.format(result_2698_inf*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = -4, -2.698 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(-3.3, .04, r'{0:.2f}%'.format(result_ninf_n2698*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/entireboxplotNormalDistribution.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explaining Inner Fence, Outer Fence, IQR Math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Idea is to have all the math in one place just to show people. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative Infinity to Positive Infinity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any PDF, the area under the curve must be 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>You will also find that it is also possible for observations to fall 4, 5 or even more standard deviations from the mean, but this is very rare if you have a normal or nearly normal distribution.</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Boxplot Documentation Used"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "General boxplot documentation: https://matplotlib.org/api/_as_gen/matplotlib.pyplot.boxplot.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing Color of Boxplot: https://matplotlib.org/examples/statistics/boxplot_color_demo.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Properties of a box plot: https://matplotlib.org/examples/statistics/boxplot_demo.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How I plotted over multiple subplots: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Back No Border but have background for ax text: https://stackoverflow.com/questions/27531290/remove-matplotlib-text-plot-border"
   ]
  }
 ],
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